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#### Properties of a coincident-time curve

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Proceedings Papers

Paper presented at the ISRM International Symposium - EUROCK 93, June 21–24, 1993

Paper Number: ISRM-EUROCK-1993-032

... testing results. 4 CONCLUSION Jointed rockmasses will present obvious dilatancy phenomenon before failure; the kickpoint value in volumetric

**curve**will increase with the increment of confining pressures, generally, σo is about 0.6 – 0.9**times**of the peak strength value. There are two failure models...
Abstract

ABSTRACT: This paper firstly describes the results of physical simulation tests about the strengh property and the deformability of the rockmasses with four types of ordered joint sets in them and then puts forward a new constitutive damage-fracture model as well as its evolution equation. The paper, in addition, describes the corresponding FEM programme for the analyses, the comparison calculation shows that the testing results and calculating ones are well coincident. RÉSUMÉ: Les resultats de simulation physique pour les proprietees de resistance et de deformation de massif rocheux avec quatre types d'ordre joints sets sont presentes dans cet article. Un nouveau model constitutif de dommage-fracture et leur equation evolue pour les massifs rocheux fissures est propose. Le programme correspondant par la methode d'elements finis pour I'analyse est intriduit, la comparaison de calcul montre que le resultat d'essais et celui de calcul est bien coincident. ZUSAMMENFASSUNG: lm vosliegenden Aufsatz wesdwen die Ergebnise ueber physikalish Simulier-Unter-suchung der Festigkeit und Deformations der Felsmassife mit den vier Typen der geordneter Klutschar beschreiben. Ein neuer, kunstitutiunell Schad-Brucksmodel und Evolutionsgleichung wird ausgestellt. Die Asbeit zeigt auβerdem eine entsprechend Programrn der Finite-Element-Methode fur ein Model; die Gegenueberstellung mit die Ergebnisse der Berechnungsverhalten und der experimentellen Modelluntersuchungen entsprechend ist. 1 INTRODUCTION Most of rockmasses encountered in engineering are jointed, nothing more than that the joint sets have developed to different extent. These joint sets were mostly formed in very long previous geological structural movements, so there exists a certain regulation about the orientation and the scale of the sets. The emphasis will be put on researching ordered joints in this paper. The strength property and the deformability of jointed rockmasses are affected by many factors, so physical simulation tests should be carried out first to get a certain law and then, based on this to find an effective analyzing method. At present, the method combining damage mechanics and fracture mechanics to analyze strength property and deformability of jointed rockmass is very promising, at which this paper aims. 2 PHYSICAL SIMULATION TESTS ON JOINTED ROCKMASSES 2.1 Tests on basic property of simulating material The simulating material should be similar with prototype rockmass in basic mechanical properties, i.e. it should follow the similarity law; besides, the material should have a constitutive curve similar with the prototype's. It should be especially noted that the simulating material should have the dilatancy property corresponding to the prototype. Many researchers either pay less attention to this or have not mixed this kind of material. Having tried and tested for ages, we have successfully mixed a simulating material consisting of yellow sand, barite powder and polyvinyl with white latex in a fixed mixture proportion. The whole jointed model is composed of many small blocks, some or them are cemented together and some are free. 3 DAMAGE-FRACTURE MODEL AND ANALYSIS ON IT 3.1 Damage-fracture constitutive model A damage-fracture model (Li & Zhu, 1992) will be introduced to analyze the previously stated testing results. 4 CONCLUSION Jointed rockmasses will present obvious dilatancy phenomenon before failure; the kickpoint value in volumetric curve will increase with the increment of confining pressures, generally, σo is about 0.6 – 0.9 times of the peak strength value. There are two failure models, for a lower confining pressure, the rockmass failure will take place longitudinal split form; which for a higher confining pressure tensile cracks will result longitudinally (along σ1 direction) at crack tips and then shearing failure will take place through the rock bridge along the crack orientation.

Proceedings Papers

Paper presented at the 3rd ISRM Young Scholars Symposium on Rock Mechanics, November 8–10, 2014

Paper Number: ISRM-YSS-2014-014

... deformation is very sig- nificant; water greatly enhanced the rocks' creep

**property**. Figure 3 indicated that creep deformation of dry specimen presents attenuation creep and 0.4 saturation 'b 0.3 t: ·~ 0.2 "' dry ~ ~ 0.1 0.0 0 4 8 12 16**time**I h Figure 2. The creep**curves**when CJ= 12.3 MPa. 0.65 saturation N...
Abstract

ABSTRACT: Moisture condition is an essential factor to mechanical properties of rock creep. Carbonaceous slates in wooden village ridge tunnel of Lan-Yu railway were taken for research object, studied the moisture condition affects the mechanical properties of rock creep through the uniaxial compressive creep tests of dry and saturated rock specimens. The test results indicated that the creep strain of saturated specimens is considerably larger than dry specimens under the same stress level. It is deformation were more than 3 times to dry specimens, and also need a long time to get into the stable creep stage. Furthermore, in terms of the creep properties of rock in dry and saturated state, put forward a nonlinear visco-plastic body, combined with Burgers rheological model, established a nonlinear damage rheological model. Meanwhile, the test results are fitted to obtain the rheological parameters of rock by taking that combined with linear decreasing weight Particle Swarm Optimization (PSO) and Levenberg-Marqud (L-M) nonlinear least squares method, fitting curves are coincide with the test curves, it shows that the proposed nonlinear rheological model is available and reasonable. 1 INTRODUCTION In recent years, rock engineering gradually towards on the deep underground, groundwater impact on the long-term stability of the rock engineering is more prominent. Research shows that water is the important factors that influence on the rheological properties of the rocks (LIU 1994). The disturbance of surrounding rock caused by tunnel excavation give rise to change of stress states, rock mass damage gradually accumulation until produce cracks what leading to the increase of the rock mass seepage path, the cracked rock mass further produce larger crack under the action of fissure water, with the increase of time, the rock engineering may be lead to engineering accidents such as instability of surrounding rock as well as the dam failures in certain states. Therefore, the long-term stability of the rock mass engineering depends on not only the action of the rheological behavior of rock, but also considered the effect of groundwater on the rheological process.

Proceedings Papers

Paper presented at the ISRM International Symposium - 5th Asian Rock Mechanics Symposium, November 24–26, 2008

Paper Number: ISRM-ARMS5-2008-124

... takes place which is

**coincident**with an increase in mechanical**properties**of shotcrete lining; therefore, the most critical point may occur before the full strength of shotcrete is reached. Since the conventional CCM does not takes the**time**-dependent stiffness of shotcrete lining into account...
Abstract

ABSTRACT Shotcrete lining is one of the most frequently used tunneling supports. As shotcrete lining is placed near the excavation face, the radial pressure on the lining develops when the excavation face advances through time. Furthermore, the mechanical properties of shotcrete lining increases over time, which make the problem more complicated. This paper presents a new analytical-numerical method which can solve the convoluted interaction of shotcrete lining and surrounding rock mass. In this work, by using a general equation indicating the structural behavior of shotcrete lining, the expression of radial pressure inside the lining versus radial wall displacement is obtained. The proposed method develops the reaction curve of the supported tunnel considering the effect of shotcrete hardening, the face advancement rate, and therefore the gradual loading on tunnel lining; thus, the reaction curve of the supported tunnel substitutes for the ground response curve and shotcrete lining reaction curve. Inasmuch as the interaction problem has numerous parameters, in no way is it possible to obtain an analytical solution. As most of the existing elasto-plastic solutions for tunnel problems in Hoek-Brown media consider an intact rock, because of numerical nature of the proposed method, the interaction of shotcrete lining with the generalized Hoek-Brown materials is also possible. Finally, an example has illustrated how this method works. Introduction Tunnel excavation disturbs the state of stress and the ground stiffness around the opening. Ground-support interaction is a consequence of resistance with which the support reacts against the movement of the surrounding ground into the excavated opening. Estimation of the support required to stabilize a tunnel opening, especially in the vicinity of the tunnel face, is an essentially 4 dimensional problem. Since the behavior of the rock mass is time-dependent, the tunnel problem is no longer three dimensional. Moreover, as the properties of the surrounding ground has significant effect on the loads acting on a liner, the ground support interaction is not just a structural problem and requires thorough understanding of both the ground and support behaviors. The study of the interaction between support structures can easily be carried out by simplified plane strain models, which are strongly dependent on the assumed degree of ground stress relief at the time of lining installation. The ‘convergence-confinement’ method (CCM), based on the simplified assumption of a circular tunnel in a hydrostatic stress field, is such a tool (AFTES, [1]). This method is discussed later in detail. Nowadays shotcrete lining is widely used as a first and fundamental support element for tunnels driven by conventional excavation methods in rock masses. The shotcrete lining is generally applied near the tunnel face when a part of the load that is distributed around the excavation is carried by the face itself. As the tunnel face advances, by decreasing the face effect, the gradual loading of shotcrete lining takes place which is coincident with an increase in mechanical properties of shotcrete lining; therefore, the most critical point may occur before the full strength of shotcrete is reached.

Proceedings Papers

#### Pressure Transient Analysis in Gas Condensate Reservoirs Producing Under Three Phase Flow Conditions

Publisher: Society of Petroleum Engineers (SPE)

Paper presented at the SPE Asia Pacific Oil and Gas Conference and Exhibition, October 8–10, 2002

Paper Number: SPE-77950-MS

... inch long cores their application to the hundreds of acres of drainage area is not an easy task. Engineers involved in reservoir simulation know that how hard it is to get a good history match and how many

**times**relative permeability**curve**has to be tuned to achieve it. Once obtained, does...
Abstract

Abstract This paper shows how to establish correlation between effective permeability as a function of pressure using well test analysis techniques in three-phase gas-condensate systems. Rigorous mathematical treatment led to correlations to estimate pseudopressure for gas condensate fluids that also use surface production data. The main purpose of developing correlation from well test analysis techniques is to use it in well performance analysis in such systems. Thus pressure transient techniques are helping to establish the flow behavior of gas condensate systems in their later life. Reservoir properties can also be estimated, however, to estimate absolute permeability, knowledge of relative permeability is required. Three-phase gas condensate systems include water producing gas condensate reservoirs. Such wells are often equipped with artificial lift to unload the produced water. To model such a three-phase flow, relative permeability curves are needed. Getting relative permeability curves becomes further demanding when reservoir conditions of pressure and temperature coincide with near critical conditions. Analysis of pressure data in such multi-phase systems requires the exact knowledge of the individual phase surface rate, which itself is a demanding task and requires the separator and stock tank properties of gas and liquid phase. In this paper we have eliminated the knowledge of individual phase surface rate. Instead, we have developed models that use the surface measured rate of these phases. Finally, an example is solved to show the use of the new technique developed. Introduction Analyzing well test data and forecasting production in gas condensate systems can be very challenging task due to phase changes that occur with depletion. This is further complicated by the retrograde behavior of light hydrocarbons and the development of very low saturation of the liquid condensate that creates a rim of the liquid around the wellbore. The immobile liquid, until it reaches a mobile saturation, can severely reduce the gas well deliverability, the primary production of such wells. Thus along with the change in physical properties of the fluids, phase change has to be handled mathematically too. If the well is produced at BHP well below the P*, the pressure at which liquid condensate is mobile, condensate rim will develop well inside the reservoir. Deliverability loss in such conditions is mainly due to three reasons: Gas undergoing liquid phase and permeability impairment by the liquid. gas undergoing in solution in developing liquid. Furthermore, to analyze multiphase systems we need relative permeability data. Since relative permeability curves are developed on few inch long cores their application to the hundreds of acres of drainage area is not an easy task. Engineers involved in reservoir simulation know that how hard it is to get a good history match and how many times relative permeability curve has to be tuned to achieve it. Once obtained, does not guarantee the accurate forecasting. In this study we used well testing based effective permeability as a continuous function of pressure. The use of relative permeability curves requires the prior knowledge of the fluid saturation. In this paper we simulated the gas condensate well test using Sapphire well test analysis software. The pressure data then was used to get effective permeability using oil, gas, and water rate data. Thus an equation for effective permeability as a function of pressure was obtained and used in evaluating pseudopressure integral. Literature Review Ramey and Hussainy 12 first introduced the concept of pseudopressure function that integrates the fluid properties as a function of pressure. Penuela 6 , and Gringarten et al. 11 discuss the well test analysis in gas condensate reservoirs. Model Description The flow from a gas condensate reservoir into the wellbore is the contribution of three distinct regions separated by time and pressure dependent flow boundaries. These boundaries, during pseudosteady state, are created by the depletion. During a pressure transient test these boundaries can be very weak and spread over a long transition zones unlike sharp solid boundaries such as fault etc., whose effect on pressure curve can be felt by the rapid change in the slope. For mathematical modeling purpose these boundaries, however, may be treated as sharp boundaries.

Proceedings Papers

Publisher: Society of Exploration Geophysicists

Paper presented at the 1994 SEG Annual Meeting, October 23–28, 1994

Paper Number: SEG-1994-0346

... ABSTRACT No preview is available for this paper. optimum value conductivity chargeability optimum loop radius

**coincident**loop frequency parameter negative response em**time**constant cole-cole parameter magnitude loop radius largest peak**time**constant electrical**property**...
Proceedings Papers

Paper presented at the SPE/AAPG/SEG Unconventional Resources Technology Conference, August 1–3, 2016

Paper Number: URTEC-2460462-MS

... geologists for a long

**time**since it was treated as true geological entities by Schaller and Henderson in 1932. In the recent Moscow 21 st World Petroleum Council, the anhydrite related hydrocarbon resource became the hot point for the meeting. Some countries like Angola, Turkey and Norway, even discussed...
Abstract

Summary Gypsum is important for hydrocarbon exploration in carbonate-evaporite basins, because it usually coexist with source and reservoir rocks. The plasticity of gypsum can cause the formation of tectonic traps, in addition with its good capping ability, effective assemblage of source-reservoir-caprock-trap may be formed. Leikoupo Formation in Longgang Area of Sichuan Basin belongs to evaporative platform to lagoon sediment system, which has large area of gypsum. Exploration achievements indicate that the discovered gas in Leikoupo Formation are mainly distributed around gypsum pots on the slope of palaeohighs, which shows superior prospect of hydrocarbon potential in this area. Based on core observation, well drilling and logging and 3D seismic data, it can be found that gypsum of Leikoupo Formation has significant geophysical response, including well logging response and seismic response. Gypsum has high values in density curve and natural gamma ray curve. Using the two well logging response, a distinguish plate was made to predict the vertical distribution of gypsum. The predicting coincidence rate can reach 90%. Gypsum shows characteristics of strong aptitude, low frequency and middle-to-low continuity. The seismic amplitude properties is sensitive to gypsum after adjusted by wells. Combined with four amplitude properties selected according to their high coefficient of correlation with wells data, the plane distribution of gypsum was predicted. Compared with the anhydrite map revealed by well data, the prediction result is satisfying. The anhydrite is helpful for the forming of dolomite and dolostone reservoirs, which can be seen from the distribution map of T2l3 anhydrite and dolostone reservoirs in T2l3 and T2l4. Introduction Anhydrite has drawn attentions of petroleum geologists for a long time since it was treated as true geological entities by Schaller and Henderson in 1932. In the recent Moscow 21 st World Petroleum Council, the anhydrite related hydrocarbon resource became the hot point for the meeting. Some countries like Angola, Turkey and Norway, even discussed the exploring cooperation area with anhydrite separately. Globally, there are many giant oil and gas fields with anhydrite as cap rocks in North American, Middle East, Siberia. Things are similar in Sichuan Basin southwest China. In the discovered nine large gas fields in Sichuan Basin, only two of them are capped directly by mud rock, the last seven are all covered by anhydrite strata. The hydrocarbon resources in anhydrite related reservoir account for 86.8% of the total proved resources. Zhao et al. (1999) pointed out that in the basins with evaporite rocks, 46% of the basins generate hydrocarbon below the evaporite layers, 41% overlap the evaporite layers, and 13% between the evaporite layers.

Proceedings Papers

Publisher: Society of Petroleum Engineers (SPE)

Paper presented at the SPE Latin American and Caribbean Petroleum Engineering Conference, July 27–31, 2020

Paper Number: SPE-198974-MS

.... The IPR

**curve**represents the contribution capacity of the reservoir to the well at a given**time**in its productive life, said capacity decreases over**time**due to different factors such as the deletion of pressure due to the production of fluids, the reduction of permeability in the vicinity of the well...
Abstract

The current demand for fossil fuels will promote the search for techniques to increase hydrocarbon production, so methods are needed to accelerate the development of this resource. The use of computer tools in the oil industry is indispensable today; we use increasingly powerful algorithms that perform extremely complex analyzes, which enable us to obtain solutions to previously affected problems pending in the industry. Most of the time the lack of parameters forces engineers to limit the study of a well, making restrictions and predictions not so accurate, especially regarding production; Based on this, the main objective is the development of a computational tool that allows to calculate the production potential of the wells drilled in the Huyapari field, which will use the python programming language, encoded from such a way to perform the calculations under the statistical methods of the analogous wells, the Joshi equation and nodal analysis. This tool is divided into two phases: the first is the calculation of the potential for pre-drilling and post-drilling of wells; the second phase is the adjustment of the potential that is carried out by means of the individual nodal analysis of each well taking into account the current reservoir pressure and the immersion limit of the pump.

Proceedings Papers

Publisher: Society of Exploration Geophysicists

Paper presented at the SEG International Exposition and Annual Meeting, September 15–20, 2019

Paper Number: SEG-2019-3215649

... trending of Acoustic

**Time**Difference (AC) of the bedding-developing formation back to the actual position, a correction method is demonstrated according to discrete wavelet transform (DWT), which merges the low-frequency signal of the neutron**curve**and the high-frequency signal of the sonic**curve**...
Abstract

ABSTRACT The complex bedding textures of shale have been confirmed to cause acoustic attenuation during propagation so that the sonic logging tool can only receive the second wave or subsequent signals instead of the first wave, which shall result in an abnormal increase of acoustic wave value in the bedding developing area. From the point of petrophysics, the real AC value should satisfy the sum of the product of each formation component’s volume percentage and its theoretical response value. Comparing the measured AC value with the theoretical value of AC derived from cores (ACtheory), when bedding textures are developed, there will exist obvious deviation. Meanwhile, the envelope of the three porosity log curves (sonic, neutron, density) should approximately coincide in normal formation, but in bedding-developed area, sonic log will be greatly affected while neutron log won’t be because of different measuring mechanism. In addition, the neutron log is investigated to be coincident with ACtheory. Hence, considering ACtheory from cores as a bridge, the development of bedding texture can be identified by the abnormal deviation of sonic and neutron logs. On this basis, to restore the real variation trending of Acoustic Time Difference (AC) of the bedding-developing formation back to the actual position, a correction method is demonstrated according to discrete wavelet transform (DWT), which merges the low-frequency signal of the neutron curve and the high-frequency signal of the sonic curve. This study firstly proposes an identification method for the development of bedding textures in shales based on porosity logs (sonic and density logs) and rock volume model then provided a new insight to restore the real AC variation trend, which effectively avoids the limitation of core analysis in laboratory and has a great significance on the following reservoir prediction, evaluation, and transformation. Presentation Date: Tuesday, September 17, 2019 Session Start Time: 1:50 PM Presentation Start Time: 4:45 PM Location: 305 Presentation Type: Oral

Proceedings Papers

Paper presented at the The 26th International Ocean and Polar Engineering Conference, June 26–July 2, 2016

Paper Number: ISOPE-I-16-193

... dynamic fracture

**properties**of cracked structures subjected to transient impact load. The peak value of the DSIFs**curve**was found to be about 2.5**times**of those under static load with the same load magnitude. Therefore, the static results may overestimate a crack as safe to propagate when it subjected...
Abstract

Abstract To aim at the evaluation of the dynamic stress intensity factors (DSIFs) for the central through cracked plate under transient uniaxial tensile loads, an analysis procedure of combining dynamic finite element analysis process and the interaction integral method is used to calculate the DSIFs. By utilizing the CINT command of the ANSYS that can calculate the static stress intensity factor, APDL of ANSYS is used to evaluate the DSIFs. As verification, this analysis procedure is presented to obtain the DSIFs and compared with Lin's solution. A good coincidence has been found between the numerical results of the paper and the reference solutions. Then, the influence of crack length, crack angle, location of the crack, impact load magnitude on the DSIFs are investigated and discussed. Introduction Dynamic stress intensity factors (DSIFs) are crucial fracture parameters in understanding dynamic fracture properties of cracked structures subjected to transient impact load. The peak value of the DSIFs curve was found to be about 2.5 times of those under static load with the same load magnitude. Therefore, the static results may overestimate a crack as safe to propagate when it subjected to transient impact load. In the naval architecture and ocean engineering, the cracked engineering structures will inevitably subjected to impact load during the service life, such as slamming or other forms of impact load. The dynamic response of a crack subjected to impact load not only needs to consider the inertial effect, but also needs to consider the spread of stress wave in the structure. Therefore, the dynamic fracture problem is more complex than the static fracture one. The dynamic fracture problems can be summarized as two categories: one is the initiation of crack under impact load; the second is the rapid crack propagation and crack arrest under impact load. It is great significance to accurately obtain the dynamic stress intensity factors (DSIFs) to investigate the crack initiation and propagation when the crack subjected to transient impact load. Chen (1975) used the Lagrangian finite difference method (FDM) to solve the DSIFs of the central through cracked plate. Then, this problem becomes the benchmark problem of studying the DSIFs. Kishimoto (1980) proposed a modified J-integral to calculate DSIFs in conjunction with the finite element method (FEM). Murti (1986) combined quarter point elements (QPE) and used the FEM to investigate various problems and the effect of QPE size to DSIFs. Dominguez (1992) used time domain boundary element method with singular quarter-point boundary elements to obtain DSIFs. Lin (1993) used the Lagrangian FDM to calculate the Chen's problem. They firstly contended the existence of the first peak of DSIFs curve. Fedelinski (1994) proposed the J-integral to obtain DSIFs by means of the dual boundary elements method. Belytschko (1995) used the Element Free Galerkin (EFG) method to calculate the DSIFs. Rousseau (2001) applied numerically and experimentally ways to obtain DSIFs for nonhomogeneous materials. Wu (2002) extended the J-integral and EFG method to calculate a single edge cracked panel under step loading. The material gradients and dynamic effects were considered in their work. Enderlein (2003) used FEM to obtain DSIFs for two-dimensional (2D) and 3D cracked bodies under impact loading. Fedelinski (2004) used the relationship between path independent integral and crack opening displacements (COD) to obtain DSIFs. The interaction integral method (Sun, 2006; Wang, 2014; Yu, 2015) was used to obtain DSIFs for homogeneous and non-homogeneous materials in recently years.

Proceedings Papers

Publisher: Society of Petroleum Engineers (SPE)

Paper presented at the SPE California Regional Meeting, March 25–27, 1981

Paper Number: SPE-9903-MS

... Abstract Strange behavior has been noticed in press r buildup

**curves**for gas wells producing from very low permeability, high drawdown formations. The typical permeability, high drawdown formations. The typical unit slope on a log-log graph of real gas pseudopressure m(p) vs**time**for wellbore...
Abstract

Abstract Strange behavior has been noticed in press r buildup curves for gas wells producing from very low permeability, high drawdown formations. The typical permeability, high drawdown formations. The typical unit slope on a log-log graph of real gas pseudopressure m(p) vs time for wellbore storage-dominated pseudopressure m(p) vs time for wellbore storage-dominated data becomes very steep (greater than unity) before going through a transition to the semilog straight line. A study of this behavior was made by means of a one-dimensional radial mathematical model wherein wellbore storage is treated rigorously. It was detected that buildup cases characterized by moderate to high pressure drawdown before shut-in always exhibit a shift of the conventional log-log graph to a larger value of the dimensionless wellbore storage constant, compared to the liquid solution. The typical unit slope in the wellbore storage control period is still preserved, and after that period, the buildup curve preserved, and after that period, the buildup curve coincides smoothly with the constant physical properties liquid case. In extreme pressure drawdown cases, properties liquid case. In extreme pressure drawdown cases, in addition, a more significant shift is also followed by a steepening towards the liquid solution. Introduction Increasing natural gas requirements and prices have stimulated interest indeep, low-permeability gas reservoirs. Pressure tests in such formations are often characterized by very high drawdown of hundreds of atmospheres. The high drawdown causes new consequences. One is a reduction in permeability in low permeability stress-sensitive formations. The effect on conventional pressure transient analysis methods has already been discussed. Recently, strange field buildup results have been observed for high drawdown gas well cases. Figure 1 shows a log-log type curve for such a case. The bend upwards from the unit slope resembles cases wherein the wellbore storage begins to decrease. Changing wellbore storage has been discussed in the literature for liquid flow cases. It was decided to study this new behavior by new transient gas flow solutions which incorporate a more rigorous material balance on the wellbore. METHOD OF INVESTIGATION The theoretical investigation was made by a numerical model. Briefly, the model simulates radial real gas flow with a fully-penetrating well located in the center of a circular slab reservoir of constant thickness. Wellbore storage is treated rigorously by considering a static column for the wellbore (see Appendix). A damaged region is modeled by an annular region of different permeability concentric with the well. A non-darcy flow effect is included by a Forcheimer-type flow equation, and a stress-sensitive formation is characterized by permeability as a function of pressure. The mathematical problem was expressed by means the following dimensionless quantities: (1) (2) (3) (4) (5) (6) P. 197

Proceedings Papers

Publisher: Society of Exploration Geophysicists

Paper presented at the SEG International Exposition and Annual Meeting, September 15–20, 2019

Paper Number: SEG-2019-3216246

... velocity model or

**time**- consuming picking. The STA/LTA traces of the data are stacked along these moveout**curves**and an event is detected when the stacked trace exceeds a threshold value. For each detected event from the surface data we look for a**coinciding**detection in the borehole data...
Abstract

ABSTRACT Microseismic monitoring from borehole and surface receiver arrays at the same time provide two different perspectives on a reservoir but may lead to unequal results that may affect the final interpretation. We currently work with a data set that consists of simultaneously recorded borehole and surface data from hydraulic fracturing. We also have catalogs of event positions and origin times that only show few coinciding event locations and detection times, respectively. Our aim is to detect microseismic events in both data sets and to find corresponding detections in each of the other data set. For borehole data we use the standard short-term to long-term average (STA/LTA) analysis. For surface data we construct moveout curves for the most coherent signals along which the STA/LTA traces are stacked. Events are detected where the stacked traces exceed a predefined threshold value. The moveout parameter are directly estimated from the data without the need of additional information on the velocity structure or time-consuming picking. For each detection, we look for a coinciding detection in the other data set at corresponding times. This way we obtain a list of coinciding detections from the surface and the borehole data, respectively, that can further be used for joint analysis of simultaneously recorded surface and borehole data. Presentation Date: Tuesday, September 17, 2019 Session Start Time: 8:30 AM Presentation Start Time: 10:35 AM Location: 303B Presentation Type: Oral

Proceedings Papers

Publisher: Society of Exploration Geophysicists

Paper presented at the 2016 SEG International Exposition and Annual Meeting, October 16–21, 2016

Paper Number: SEG-2016-13960017

... the application of a series of field VSP data, we can see that the Q

**curve**of CFS method**coincides**with geological layers better than those of the others, which are hardly to reflect the main attenuation trend. Presentation Date: Monday, October 17, 2016 Start**Time**: 4:35:00 PM Location: Lobby D/C Presentation...
Abstract

ABSTRACT The seismic attenuation characterized by Quality Factor (Q), is one of the key properties to reveal different stratums. This paper is aimed at discussing influencing factors of Q inversion and providing references for practical application. We elaborate three different methods to inverse Q value with VSP data, including Centroid Frequency Shift (CFS) method, Spectral Ratio (SR) method, and Amplitude Attenuation (AA) method. Comparison between the results from CFS with the other two methods is conducted on frequency band width, high Q value layers, wave field components, interface interference and thin layers. Results show that, CFS method is more stable and accurate than the other two methods for dealing with different wavefields, thin and high Q layers. Frequency band width influences inversed effects of all the three methods. The band wider, the results better. Moreover, from the application of a series of field VSP data, we can see that the Q curve of CFS method coincides with geological layers better than those of the others, which are hardly to reflect the main attenuation trend. Presentation Date: Monday, October 17, 2016 Start Time: 4:35:00 PM Location: Lobby D/C Presentation Type: POSTER

Proceedings Papers

Publisher: Society of Petroleum Engineers (SPE)

Paper presented at the SPE/IATMI Asia Pacific Oil & Gas Conference and Exhibition, October 20–22, 2015

Paper Number: SPE-176101-MS

...

**time**while dual porosity model took six days. Dual porosity model needs longer run**time**due to complex solver equation to accommodate both matrix and fracture**properties**. In conclusion, single porosity model gives better match and reasonable run**time**compared to dual porosity model. It is decided...
Abstract

A practical method to adapt fractures both micro and macro as flow enhancing properties in a single porosity model is introduced to simulate Ujung Pangkah fractured carbonate reservoir. This approach is taken because dual porosity modeling attempt fails to explain the behavior of many wells which experience early water breakthrough and/or excessive water production in Ujung Pangkah field. The enhancement factor term is used to define the degree of permeability enhancement by diffuse or micro fractures. At well location, the enhancement factor can be determined by the ratio of production test to the production of matrix-only model. The enhancement factor 3D distribution is derived from well data and seismic minimum curvature attributes as trend. Fracture corridors correspond to macro fractures in the order of meters extending vertically and/or laterally. As normally scattered spatially, fracture corridors cannot be modeled in a discrete fracture network model which is the integral part of dual porosity model. Some wells show behavior anomalies, such as rapid, early water breakthrough with excessive water production in unlikely location. It is observed that the location of these anomalies coincide with the fracture lineaments derived from the seismic incoherency attribute. As the fractures are well characterized, diffuse fractures as permeability enhancement and fracture corridors as high permeability streaks, the further improvement of history match is then easily achieved by calibrating two other key parameters; relative permeability curves and aquifer strength. The relative permeability is calibrated to the shape of fracture relative permeability. Oil rate match is greatly improved. Water rate match is achieved by placing adequate aquifer strength. Reservoir dynamic of Ujung Pangkah carbonate fractured reservoir can be simulated as a single porosity model with permeability enhancement adapted from two types of fracture distribution. Diffuse fractures enhance the overall permeability and fracture corridors dominantly influence flow dynamic in certain local area. Compared to dual porosity model, adapting fractures as permeability enhancement in single porosity model is more practical, more efficient in simulation run time – computational cost.

Journal Articles

Journal:
SPE Reservoir Engineering

Publisher: Society of Petroleum Engineers (SPE)

*SPE Res Eng*9 (02): 85–91.

Paper Number: SPE-22904-PA

Published: 01 May 1994

... carbide were used. Silicon carbide was the preferred medium for measurement of K o values because it was essentially inert and constant results were obtained on repeated tests. The long

**time**required to precondition and equilibrate live brine and oil with consolidated and disaggregated cores made those...
Abstract

Summary A single-well tracer test (SWTT) that uses soluble amounts of in-situ-generated CO 2 as the oil tracer is described. Water-soluble-only injectants simplify test interpretation and improve residual-oil-saturation (ROS) determination. The CO 2 -generator chemistry allows the test to be tailored over a wide range of injectivities and reservoir temperatures. Introduction This paper documents a new single-well tracer chemistry that uses hydrolysis of halogen-organic acid salts as a means to generate CO 2 and to trace ROS. 1 The availability of generators with different, well-behaved hydrolysis rates allows the test to be tailored to each individual well. Suitable water tracers include methanol, tritium, bicarbonate, or the spent CO 2 generator. Field results demonstrate test application and interpretation. Comparison of Ester and CO 2 Technology Figs. 1a and 1b schematically present the generalized positions of the tracers used in the ester and CO 2 systems at the end of the displacement step relative to the wellbore. Note in Fig. 1a that the ester is "overflushed" during injection and then "back-overflushed" by the displacement brine during production. In the CO 2 system (Fig. 1b), the generator chemicals are water-soluble-only when injected. Thus, the reactive and nonreactive tracers travel together, remain in front of the displacement brine during injection, and have locations that always coincide beyond the injection-fluid-cooled near-wellbore region at pump shutdown. Ester chemistry calls for injection of a reduced-volume "minitest." If the mini test shows some return of injected nonreacting tracer and the presence of generated tracer, a full volume "main test" is run. 2 With the CO 2 -tracer chemistry, however, a minitest is unnecessary because the reaction rates of the acid generators are more predictable downhole than are ester reaction rates. The Appendix provides more information on CO 2 -generator kinetics. Little difference exists in field operations with either tracer system. Similar procedures and equipment (Le., injection pumps, storage vessels, and test separators) are used and other chemically distinct nonreacting water-soluble-only tracers may be added at various stages of the injection sequence to aid in interpretation and to address well- and reservoir-specific questions. Although CO 2 generators are more expensive than esters, chemical cost is a small fraction of SWTT expense in either case. Partition Coefficient Properties and Determination The partitioning nature of CO 2 is nearly ideal for ROS determination. K o is ˜3 and is relatively insensitive to salinity and temperature. The oil-tracer profile is well-defined and adequately separated from the water-tracer profile for sensitive ROS measurements. Figs. 2 and 3 show that the differential change in K o for CO 2 is 0.01 and 0.008 nondimensional units per 1,000 ppm NaCl and 1°F change, respectively. Fig. 4 indicates that there is essentially no differential change in K o with CO 2 concentration in the range studied. Frontal analysis was used to obtain the CO 2 K o values between methane reconstituted crude and synthetic reservoir brine. 3 Consolidated Berea and Bentheim cores and sandpacks made from Berea cores, Clemtex No. 5 sand (a well-sorted and rounded fine sand), or ground silicon carbide were used. Silicon carbide was the preferred medium for measurement of K o values because it was essentially inert and constant results were obtained on repeated tests. The long time required to precondition and equilibrate live brine and oil with consolidated and disaggregated cores made those materials too costly to work with on a regular basis. Eight K o measurements on reconstituted crude and brine at reservoir conditions yielded a value of 3.36± 0.15. A similar value was determined for a California crude at 200°F. The K o values did not vary significantly when stock-tank oil was substituted for live oil. Separate in-situ CO 2 -generation tests were run in preconditioned Berea cores and packs. These studies confirmed measured hydrolysis rates, K o values, and use of CO 2 as an oil-saturation tracer. Multiple flow tests run in cores containing carbonate materials with no oil present showed that the CO 2 propagated at the same rate as tritiated brine. Interpretation of Tracer Response During production, the generated CO 2 is retarded by the oil and separates from the water-soluble-only tracers that return directly through the water. Assuming that (1) the flow pattern is reversible, (2) the hydrolysis rate of the reacting tracer is constant during the process, and (3) the main part of the reaction occurs during the soak period, the ROS can be calculated from the differential response of the two tracers and K o . The governing equation is Equation 1 where V oi and V wi are the associated tracer-determined arrival volumes. V oi is always greater than V wi (unless there is no oil in the reservoir; then V oi =V wi ) because it takes more production volume to transport the partitioning tracer back to the wellbore than for the nonpartitioning tracer. When the V oi /V wi ratio in Eq. 1 is constant throughout tracer production, the required quasistatic equilibrium condition for application of chromatographic principles is satisfied and S or is uniquely determined. In the ideal case (Gaussian-shaped response curves), S or is simply calculated from the peak-to-peak tracer separation volumes and K o . Various studies, 4–9 including this one, have shown that K o can be measured with sufficient accuracy to prevent this parameter from being considered a problem in oil-saturation determination. Mathematical modeling is required for the interpretation of complex nonideal response patterns. ROS Calculation Injection of water-soluble-only tracers in the CO 2 method allows an improved oil-saturation calculation procedure compared with the iterative and possibly nonunique procedures that are required when oil-soluble esters are used. All parameters specific to the well and reservoir are determined from the water-tracer response and held constant. Next, various V oi /V wi ratios are applied to the water-tracer simulation results to calculate a series of possible oil-saturation responses. The measured and calculated oil-tracer responses are then overplotted. If an overplot match is found, Eq. 1 is the governing equation and the oil saturation is uniquely determined. Note that dispersion is the same for both oil and water tracers because they return from the same position in the reservoir through the single flowing brine phase. If the measured oil-tracer curve does not overlay one of the calculated curves (i.e., measured V oi /V wi is not constant), the test is flawed. This interpretation procedure, unique to water-soluble-only injectant tracers, provides a check on the validity of the test physics, generator chemistry, engineering design, tracer and volume determinations, well integrity, and operating procedures. p. 85–91

Journal Articles

Journal:
Journal of Petroleum Technology

Publisher: Society of Petroleum Engineers (SPE)

*J Pet Technol*40 (07): 881–886.

Paper Number: SPE-14659-PA

Published: 01 July 1988

... models of early development wells to

**coincide**with the**timing**of the pressure meas- urements. Pressure maps were generated for later models to coin- cide with anticipated completion dates of potential infIll wells. These areal pressure maps were used to optimize the placement of intill wells. The effects...
Abstract

Summary. The ability to predict incremental rates and reserves reasonably from infill development drilling in tight-gas reservoirs is enhanced through use of a three-dimensional (3D), multiwell, dry-gas model. Single-well [two-dimensional (2D)] and multiwell [three-dimensional (3D)] input and results are compared, and examples of both are presented. Measured initial reservoir pressures on an eight-well infill program compared favorably with the 3D model predictions. Introduction Upon the Federal Energy Regulatory Commission's establishment of the Sec. 107 incentive pricing, development of the Cotton Valley tight-gas-sand resource base expanded significantly, with more than 1,100 wells drilled during 1977–82. The soft gas market, coinciding with gas deregulation, slowed further development between 1983 and the present (Fig. 1). As of Oct. 1985, there were approximately 1,230 Cotton Valley sand producers on Texas Railroad Commission records for the area encompassing Harrison, Panola, and Rusk counties. Amoco Production Co. has drilled or participated in the drilling of more than 170 of these tight-gas-sand wells, situated primarily in the Blocker, Carthage, Dirgin, Henderson North, Tatum, and Woodlawn areas of the Cotton Valley field (Fig. 2). Most of this development has been on 640-acre [260-ha] density. The Cotton Valley (Jurassic) sandstone of east Texas is a series of marine and lagoonal deposits. Diagenesis in the form of calcite cementation and quartz overgrowth, combined with overburden pressure, has reduced its porosity and permeability. With permeabilities in the microdarcy range, massive hydraulic fracture (MHF) stimulations are usually required to make a commercial completion. Gas production from the east Texas Cotton Valley sands has been at depths ranging from 9,000 to 10,500 ft [2700 to 3200 m]. The gross thickness of the Cotton Valley sand/shale sequence averages 1,500 ft [460 m]. This paper discusses modeling associated with only the lowermost Yellow, paper discusses modeling associated with only the lowermost Yellow, or Taylor, zone as shown in Fig. 3, a type log from the Blocker Cotton Valley field. The model work presented here was undertaken to determine the incremental rates and reserves associated with infill drilling of existing units. Two types of reservoir models were used. The first, a 2D model, contains a single well located in the center of a rectangular, homogeneous drainage area. This model is appropriate for minimum-well-density situations. This single-well model, however, fails to account for interference from other wells, which was suspected after early infill drilling (160 to 320 acres/well [65 to 130 ha/well]) was analyzed. The second model has a 3D capability that allows areal and vertical variations in reservoir properties. Most important, it can model several wells at once, thereby providing the opportunity to determine realistic estimates of incremental production associated with new well drilling. The 3D model results were initially validated through the measurement of pressures on eight infill wells drilled during 1985. Discussion The following discussion details the basic data requirements for the model work, describes both the single-well (2D) and multiwell (3D) models, and provides an example analysis of an infill well location using both models. The single-well model was used to provide historical performance matches of existing wells for later use in the multiwell model. The single-well model can also be used to predict reserves of a proposed infill well. The modeling comparison predict reserves of a proposed infill well. The modeling comparison section of this discussion illustrates the benefits of using the multiwell model vs. the single-well model for the determination of infill-well reserves. Gas Properties. Separator tests from wells in each field area were used to estimate an average Yellow zone well-stream composition. Gas viscosity was estimated by Thodos-type correlations. Other gas properties were determined with the modified Redlich-Kwong equation properties were determined with the modified Redlich-Kwong equation of state. These field average properties were used in all pressure-transient and modeling efforts. pressure-transient and modeling efforts. Initial Reservoir Pressure. Estimates of initial reservoir pressure in the various field areas were determined from early well-pressure bomb measurements (greater than 140-hour shut-ins). The average pressure gradient in this Cotton Valley area equaled 0.55 psi/ft [12.4 kPa/m] (15 wells). Previous literature has documented the overpressured nature of the Yellow zone as compared with the uphole Cotton Valley sand intervals. Porosity, Water Saturation, Net Pay. Yellow zone volumetric gas Porosity, Water Saturation, Net Pay. Yellow zone volumetric gas in place was determined through detailed well log and core analyses. Some of the techniques used to estimate net pay in the Cotton Valley have been presented previously. Field average porosities and water saturations for the pay intervals ranged from 5.7 to 7.9% and from 27 to 49%, respectively. Formation Flow Capacity. Documented tight-gas-sand prefracture pressure-buildup techniques were used to analyze pressure-buildup pressure-buildup techniques were used to analyze pressure-buildup data from more than 100 Yellow zone producers. Average field values of formation flow capacity ranged from 0.39 to 0.92 md-ft [1.9 × 10(-1) to 2.8 × 10(-1) mdm]. Real-gas pseudotime and pseudopressure were used in conjunction with the equivalent-time function for the analysis. Refs. 5 and 6 detail the benefits associated with using these modified time and pressure functions in tight-gas reservoirs. Fracture Flow Capacity and Half-Length. Postfracture analysis of all available test data was attempted. Two techniques were used: the constant-rate and the constant-pressure type curves developed by Agarwal et al. for use in finite-flow-capacity fractures. With these techniques, values for fracture half-length, Lf, and dimensionless fracture capacity, FCD, were estimated. A third method, the scalar technique discussed by Tison et al. was also tested and found to provide some assistance in generating estimates for Lf. JPT P. 881

Proceedings Papers

Publisher: Society of Petroleum Engineers (SPE)

Paper presented at the SPE/DOE Low Permeability Gas Reservoirs Symposium, May 27–29, 1981

Paper Number: SPE-9868-MS

... and to create wider fractures. Various problems were encoun- tered in using these special fluids in deep wells where temperatures exceeded 200°F and where pumping

**times**exceeded one hour. High viscosity cross-linked gels were introduced to the petroleum industry with great expectations. Their rheological...
Abstract

Abstract Fracturing formations deeper than 10,000 feet at temperatures greater than 200 deg. F with crosslinked gels created a variety of special problems in South Texas and Anadarko Basin wells. Engineering analysis of these problems resulted in modifications of fluids systems, problems resulted in modifications of fluids systems, treatment design, and fracturing operations. These changes eliminated premature shut-downs of fracturing treatments and improved stimulation ratios. Introduction Fracturing formations deeper than 10,000 feet in the Anadarko Basin coincided with various developments in the petroleum industry in the use of high viscosity fluids to transport prop better in the fracture and to create wider fractures. Various problems were encountered in using these special fluids in deep wells where temperatures exceeded 200 deg. F and where pumping times exceeded one hour. High viscosity cross-linked gels were introduced to the petroleum industry with great expectations. Their rheological properties offered an excellent means of placing long propped fractures in low permeability sandstones. Excellent productivity increases were expected, especially in tight gas formations. Fluid properties indicated excellent suspension of prop over long distances with little or no settling. The fluid loss coefficients were believed to be extremely low, less than .001 ft/ square root min. It was believed that the leak-off was considerably less than that of conventional uncross linked gels in low permeability formations. Experience with these fluids often did not confirm expected results. Either sandouts occurred or the results of fracturing were less than expected or predicted from standard productivity curves like those of McGuire and Sikora. In early 1979, a detailed analysis was made of a number of wells in South Texas that had been fractured using cross-linked gel systems. This study showed that some or all of the following problems were encountered on 80% of the wells fractured over a one year period: Equipment breakdowns involving shutdown times of five to thirty minutes during injection of prop laden fluid. These treatments usually"pressured out" shortly after pumping was resumed. (The term "pressured out" is used asopposed to "screen out", since in most of these cases it was possible to flush down to the top perforation at a low rate and maximum pressure, indicating an obstruction at some point out in the fracture. The term"screen out" implies blockage at the perforations and an inability to flush down.) "Pressuring out" before designed treatment volume could be pumped, even without equipment malfunctions. This sometimes happened when the injected sand stage was only at 2 or 2.5 lbs/gallon. Lower than designed productivity increases even when treatments went as scheduled. Bottom hole static temperatures on these wells ranged from 230 deg. F to 290 deg. F. Pumping times were in excess of 2 hours. New rheology data were developed by the service companies based on shear time and temperature. Computer cool down studies were made which indicated the leading 60-70% of the cross-linked gel was subject to near bottom hole static temperatures. Viscosity profiles were then made for several crosslinked gel systems used in treatments where "pressuring out" problems were encountered. These profiles indicated that some of the cross-linked gel systems were extremely temperature and shear sensitive, retaining only 10 to 20 cps apparent viscosity at the fracture tip under bottom hole temperature conditions. It was also discovered that there were considerable differences in the apparent viscosities with the same polymer loading of different systems. Since the base polymer was essentially the same for most systems, it was concluded that the difference must lie in the cross-linking mechanism. Some gels seemed to have a stronger bond which made them less sensitive to shear and temperature degradation. P. 7

Proceedings Papers

Publisher: Society of Exploration Geophysicists

Paper presented at the 2000 SEG Annual Meeting, August 6–11, 2000

Paper Number: SEG-2000-1576

... and the model trace. This method can hardly solve two problems: (1) the variation of wavelet in

**time**domain. (2) the practical seismic record has something to do with lithology, petrophysical**property**, and formation sequence In this paper, we develop and present a new technique, Comprehensive Reservoir...
Abstract

Summary So far most of iteration inversion methods are based on convolution models, in which users gradually modify the wave impedance and thickness, obtain the wavelet correspondingly correction, and then, conduct forward modeling to minimize the differences between the practical trace and the model trace. This method can hardly solve two problems: (1) the variation of wavelet in time domain. (2) the practical seismic record has something to do with lithology, petrophysical property, and formation sequence In this paper, we develop and present a new technique, Comprehensive Reservoir Inversion System (CRIS). It gives priority to well logging data and uses seismic data as a constraint, and in particular, it adopts the non-linear inversion method and several quality constraints and control methods. CRIS has been verified by tens of case studies and shows these advantages: (1) high resolution; (2) accurate lateral extrapolation and multi-well tie; (3) reducing multi-solution uncertainty

Journal Articles

Journal:
SPE Drilling & Completion

Publisher: Society of Petroleum Engineers (SPE)

*SPE Drill & Compl*15 (01): 37–43.

Paper Number: SPE-62114-PA

Published: 01 March 2000

.... The proliferation of such regional datums over

**time**has meant that their areas of application frequently overlap. The same set of latitude and longitude coordinates, referenced to different geodetic datums, will refer to different points on the Earth. The coordinates alone, contrary to common belief, do...
Abstract

Summary This paper provides a review of current practices for calculating directional drilling placement in the light of modern extended-reach applications. The review highlights the potential for gross errors in the application of geodetic reference information and errors inherent in the calculation method. Both types of error are quantified theoretically and illustrated with a real example. The authors borrow established land surveying calculation methods to develop a revised best practice for directional drilling. For the elimination of gross errors they prescribe increased awareness and a more disciplined approach to the handling of positional data. Introduction When calculating well position, directional drillers currently take no account of Earth curvature. In effect, the well is planned and drilled using a "Flat Earth" model. The errors inherent in the Flat Earth assumption were until recently justifiably ignored as insignificant. However, the advent of longer wells aimed at smaller targets has prompted this more detailed analysis. The analysis shows that the errors can no longer be assumed insignificant. This suggests that in the future, oil companies will demand that the directional drilling software used for extended-reach applications incorporates more precise well positioning calculations. In defining the form of these calculations, a balance must be struck between computational complexity and real requirements. That said, the ubiquity of computers at all stages of the drilling process has virtually eliminated the need for calculations ever to be performed by hand. A Geodesy Primer Geodesy is the name given to the study of the size and shape of the Earth. The branch of land surveying which properly takes account of this shape is known as geodetic surveying. To accurately describe the effects of Earth curvature on well positioning, it is necessary to use some geodetic terminology. The standard textbook, which contains full definitions of all the terms which follow, is by Bomford. 1 The surface that is every where perpendicular to the direction of gravity (an "equipotential surface") and that on average coincides with mean sea level in the oceans is called the geoid . The geoid is much smoother than the physical surface of the Earth, but is still too irregular to be used as a reference for spatial coordinates. As an alternative, we use the geometrical shape which most closely approximates the shape of the Earth—an ellipsoid , which in this context is an ellipse rotated about its minor axis. The term spheroid is sometimes used in place of ellipsoid. To be useful as a coordinate reference, a relationship between the position of the ellipsoid and the solid Earth must be defined. Although sometimes used to refer to just this relationship, the term geodetic datum is more correctly used to include the definition of the ellipsoid as well. When combined with an axes definition, a geodetic datum defines a three-dimensional (3D) geographic coordinate system, the dimensions being (geodetic) latitude and longitude and ellipsoidal height (height above the ellipsoid). It is possible to define a geodetic datum which approximates the shape of the Earth over the entire globe. WGS 84, used by the Global Positioning System (GPS), is an example. In practice, most geodetic datums used for mapping have been defined to give a more precise fit over a restricted geographical area. As an example, coordinates of points in the North Sea are conventionally quoted with respect to European Datum 1950 (ED50), which incorporates the International 1924 ellipsoid. The proliferation of such regional datums over time has meant that their areas of application frequently overlap. The same set of latitude and longitude coordinates, referenced to different geodetic datums, will refer to different points on the Earth. The coordinates alone, contrary to common belief, do not adequately define a particular location. Lines of constant latitude and longitude are called parallels and meridians , respectively. These lines are curved in three dimensions, but may be represented on a plane by means of a projection . The rectangular coordinate system on the plane is called a grid . It is impossible to devise a projection which represents all true directions and distances correctly on the plane. However, it is possible to control this distortion so that the shapes of small areas are preserved. Projections with this property are called orthomorphic or conformal, and include the Transverse Mercator Projection and most others used for oilfield mapping. For any orthomorphic projection, the amount of distortion to directions at a point on the grid is defined by grid convergence , the angle clockwise between the meridian passing through the point (i.e., true north) and grid north. Likewise, the amount of distortion to scale at a point is defined by the point scale factor . (Not to be confused with the scale factor at the natural origin, which is a fixed parameter used in the definition of many projections. For UTM zones, its value is 0.9996). The point scale factor changes with geographical position, which results in distances calculated from grid coordinates differing from distances measured on (or through) the ground. In this paper, we shall call the ratio of map grid distance to true distance the grid scale factor . Since the arc length of a degree of latitude or longitude decreases with increasing depth, the grid scale factor ( Fig. 1 ) must increase to compensate. For nearby points A and B : The grid azimuth from A to B equals the true azimuth from A to B minus the grid convergence . The grid distance from A to B equals the true distance from A to B multiplied by the grid scale factor . Since grid convergence varies from place to place, the first of these rules is only an approximation—the error will increase as the distance between A and V grows. The second rule is always valid by our definition of grid scale factor. Vertical Coordinates. Horizontal position being defined by ellipsoidal coordinates (latitude and longitude), it seems natural to define vertical position by height above the ellipsoid. This is not done in practice, the main reason being that the surface of the ellipsoid offers no physical reference point for measurement. The geoid (roughly speaking, mean sea level) is a much more convenient surface to use as a height reference. Surveyors working on land can measure the difference in height above the geoid at two locations by spirit leveling. The reference level used as a zero datum is defined by mean sea level at a selected coastal location, or an average value of mean sea level at several locations, over a specified period of time. Elevations on land should include a reference to this vertical datum. In the U.S., it is termed the North American Vertical Datum of 1988 (NAVD88), which also covers southern Canada. In Britain it is Ordnance Datum Newlyn (ODN). Surveyors working offshore can measure elevations relative to sea level directly and, by reference to tidal predictions, correct these to mean sea level.

Proceedings Papers

Publisher: NACE International

Paper presented at the CORROSION 96, March 24–29, 1996

Paper Number: NACE-96063

... A corrosion rate was determined from the weight loss after descalling divided by the immersion

**time**and the specimen surface area. Specimens were mechanically polished with #?320 emery paper. Figure 2 shows a coupled specimen and an uncoupled specimen. A coupled specimen was joined by a bolt and a nut made...
Abstract

ABSTRACT galvanic corrosion, oil country tubular goods, carbon steel, stainless steel,corrosion rate, sour gas, CO 2 gas ABSTRACT Galvanic corrosion behavior in sour and sweet well environments for combinations of materials from carbon steels to high nickel alloys was investigated by using electrochemical methods and immersion tests. Basically, the results obtained by electrochemical methods coincided with those by immersion test. The ratio of a corrosion rate of a material in coupled to that of uncoupled defined as galvanic effect index (GEI) was studied with different surface ratios. GEI increased with an increase in the weight loss of the uncoupled specimen and is at most 2.0 in both sweet and sour environments when a surface area ratio of anode site to cathode site was 1:1. GEI increased with increasing static ratio but almost independent on surface ratio at temperatures more than 100 ºC. Galvanic corrosion was not serious as expected from the theory. INTRODUCTION In oil and gas wells, the conditions of corrosive environments vary with depth. By using a tubing string composed of different tubing materials (combination string), the most suitable material required for each depth can be chosen. Although a combination string would realize cheaper material cost, galvanic corrosion would be a concern. Extensive research for galvanic corrosion has been carried out, however, few researches on galvanic corrosion in oil and gas well environments were performed. The purpose of this study is to clarify what combination of materials can be applied without pronounced galvanic corrosion. Galvanic corrosion behavior was investigated for combinations of typical tubing materials in various simulated oil and gas environments, such as sweet and sour environments. EXPERIMENTAL PROCEDURE Material Table 1 lists the chemical compositions and the mechanical properties of materials used in this study. All the materials were properly heat ?treated. Measurements of Galvanic Current and Coupled Potential Galvanic current and coupled potential were measured using a high pressure and high temperature autoclave. A pressure?balanced outer Ag/AgCl reference electrode including O.lmol potassium chloride solution (0.lMKC1) was used. A specimen was coated with silicon resin, leaving an area of lcm 2 for measurement after mechanical polishing. Just before installing into an autoclave, the specimen was pickled in 50!Z0 sulfuric acid to remove the air-formed film at 60 t . After two specimens were installed in an autoclave, deaerated 5% sodium chloride solution (5%NaCl) was poured into the autoclave. The solution was deaerated thoroughly by nitrogen gas bubbling after the autoclave was sealed. Test gases were introduced into the autoclave after the solution reached a test temperature. The two specimens were connected after each potential of these specimens reached the steady state. Then galvanic current and coupled potential were started to measure using a potensiostat. The test apparatus is illustrated in Figure 1. The test duration was 1 week. Polarization Measurement Polarization curves were measured immediately after the test started and after 1 week. Experimental procedures were the same as the measurement of galvanic current and coupled potential. The sweep rate was 10 mV/min. Immersion Test A corrosion rate was determined from the weight loss after descalling divided by the immersion time and the specimen surface area. Specimens were mechanically polished with #?320 emery paper. Figure 2 shows a coupled specimen and an uncoupled specimen. A coupled specimen was joined by a bolt and a nut made of polytetrafluoroethylene(PTFE). In order to

Proceedings Papers

Publisher: Society of Exploration Geophysicists

Paper presented at the 1990 SEG Annual Meeting, September 23–27, 1990

Paper Number: SEG-1990-1719

..., which

**coincides**witt the front of the radiated wave at**time**zero. The wave front S propagates upward in overburden until, at the moment t,/2, it reaches the central point, A, of the array located along a seismic line A,A I position of front S of a fictitious wave is shown ix Fib. lc. An element ^E...Advertisement